Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 05 Dec 2024 11:50:15 -0500 Organization: Peripheral Visions Lines: 16 Message-ID: References: <87frn50zjp.fsf@bsb.me.uk> <87y10vzo35.fsf@bsb.me.uk> <87ser3zgez.fsf@bsb.me.uk> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="utf-8"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 05 Dec 2024 17:50:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="fd485c10c792450e6329c5a42bd0887d"; logging-data="1825940"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+zc/eHvu5prx7mPgEPiVeVRdfK83m2cbw=" Cancel-Lock: sha1:9dRnKvtf5TjpTabaGH2d+txUvoI= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2348 WM pretended : > On 05.12.2024 14:40, FromTheRafters wrote: >> WM used his keyboard to write : > >>> All means all with no exception. But every number you can take belongs to >>> a vanishing subset of ℕ. >> >> What do you mean by vanishing? > > The subset of numbers that can be taken is ℕ_def. It is smaller than > |ℕ|/k for every k ∈ ℕ. > > Have you meanwhile found an example for sequences with terms a_n = b_n for > every n but different limit? Why should I?